Fuzzy Congruence Relations on Lattice Implication Algebras

摘要

The notion of fuzzy congruence relations on lattice implication algebras is proposed and properties of fuzzy congruence relations are discussed. Secondly, equivalence characterization of fuzzy congruence relation are obtained, and, showed the fact that the fuzzy congruence is a generalization of congruence on lattice implication algebras. Thirdly, we prove that the set FF(ぷ) of all fuzzy filter is isomorphic to the set FC(ぶ) of all fuzzy congruence relations. Finally, the quotient lattice implication algebras which determined by fuzzy congruence relation is studied and homomorphism theorem is obtained.